If y=9 when x=9, how do you find y when y=-27 given y varies inversely as x?

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Answer 1 · 2017-06-12T21:16:14

$x = -3$ when $y = -27$

Inversely: $y = k/x " or using proportions: " y_1/y_2 = x_2/x_1$

Using the two step method , find $k$ given $y " and " x$ :

$9 = k/9$

Multiply both sides by $9$ to eliminate the denominator on the right:

$9 * 9 = k/9 * 9/1$

$81 = k$

Now fill in the equation using $k$ :

$(-27)/1 = 81/x$

Find $x$ by using the cross product: $-27x = 81$

Divide both sides by $-27: " "(-27x)/-27 = 81/-27$

$x = -3$

Using Proportions: $y_1/y_2 = x_2/x_1$

$9/-27 = x/9$

Use the cross product: $-27 x = 81$

Divide both sides by $-27: " " (-27x)/-27 = 81/-27$

$x = -3$